I'm relatively new to cosplay (okay, I've still yet to do my first cosplay) and I haven't really had much practice at making clothes etc. I was going to make the costume for my first cosplay, but realized I had absolutely no idea where to begin, so I chickened out and bought the costume. However, in the future I would like to make my own costume, so can anyone give me some help on where to begin? Like maybe recommend some good beginners tutorials for making basic pieces of clothing or something. I've got a sewing machine at home-though it's only a 'mini' one- and know how to work it from doing it at school, plus I do a bit of cross-stitching, so I dunno if that would help at all

a 'mini' sewing machine might not be able to handle big projects like costumes. Your best bet is to make simple things. Maybe something like doll's clothes or a type of clothing that doesn't neccessarily require a pattern.Generation T is a good place to start to get a feel for making clothing. I would recommend you get it from your library or bookstore. It doesn't primarily deal with sewing, but you'll be making clothes from used t-shirts.
...I don't know. If I were you I would hit the books (like I did. I had to teach myself.), or find someone who has made garments before. Because when you sew clothes, it can get confusing and complicated if you don't know what you're doing.

Echoing that a mimi sewing machine might not be the best for larger projects. It'll do you just fine for basic stuff and practicing (as I did use one for a long while :3), but getting yourself a new one might be something to think about as you more on to bigger stuff.
As for what to look for... looking up basic sewing tutorial online would be a great help, especially if you don't have anyone else to teach you different techniques. Though, Home Economics/sewing is good for a start~

If you're looking into making clothes, you should be able to finns beginners/easy-sew patterns in fabric shops etc. It might be an idea to ask the staff there if they can reccommend patterns for beginners

I recommend the "It's So Easy" patterns (a lot of pattern-makers have them under different names) to start off! They're more detailed with the instructions and terminology, so they're good for beginning pattern reading. If you wanting to jump into something complicated, buy muslin fabric to make mock-ups and to practice sewing with. That way you'll have practice for doing it on your real fabric and if you mess up, it's not a big deal. Muslin is also good for checking the fit of a costume before making it.

I'm seconding finding easy patterns at the store. Each brand has their own line, but Simplicity is made to be easier to start (hence the name). You'll find over time that the tailoring in the easy patterns isn't generally too fantastic, but they'll teach you the basics until you feel you can move up. Start with something like bags or pajamas, and just move up in complexity as you feel comfortable with each step. Look up tutorials online whenever you encounter a step you don't know, and you'll be sewing huge and complex costumes before you know it! ^_^

She's the one in the plaid skirt and the black coat. The basic pieces are:

A black coat - you can purchase something similar and alter it to tuck in the waist. It's a good lesson on how clothing is constructed. You could add the over-sized cuffs and button detail.
A plaid school girl skirt - an easy find
A yellow sweater vest - also relatively easy to find
White gloves - easy to find and inexpensive
A white button down shirt - who doesn't already have one?
A green striped tie - easy to make
Giant clunky boots - you can take some black boots and add the detail with white fabric or foam or some other material.

The local Salvation Army / Thrift store is your best bet for finding these items for not a lot of money. Spending a few dollars on a complete piece can sometimes be worth the frustration of making something from scratch. There is plenty of detail to be added in a costume like this - buttons, trims, proportions, hair, makeup, props etc - all that go into creating a successful cosplay. You also get some beginner sewing experience.

You can break down a lot of costumes the same way. I'd be happy to help you walk through one if you want.

Another good type of garment for practicing on are pajama pants or shorts to sleep in. You can get some flannel with a fun pattern on it, and there are usually only 2 or 4 pattern pieces that you'll need.

Thanks so much for all the advice everyone! I've had a look at Simplicity/It's So Easy, and they look quite good, so I think I'll start with some of them, and then maybe look at using the techniques I've learnt to put together a costume as well as using the way char99char mentioned